- Docente: Enrico Fatighenti
- Credits: 6
- SSD: MAT/02
- Language: Italian
- Moduli: Enrico Fatighenti (Modulo 1) Fabrizio Caselli (Modulo 2)
- Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Mathematics (cod. 6730)
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from Sep 15, 2025 to Dec 18, 2025
Learning outcomes
At the end of the module, the student has an advanced knowledge of topics such as numerical sets, polynomials and polynomial equations, algebraic structures, and is able to use various aids to support teaching.
Course contents
Integer numbers, arithmetic functions, algebraic structures in number theory, Diophantine equations, prime numbers: their distribution and asymptotic behavior.
Root systems: examples in the Euclidean plane and their classification. Root lattices and their symmetries. Semi-simple Lie algebras and their associated root systems. Dynkin diagrams. Simple Lie algebras, classical and exceptional.
Preliminary knowledge: Fundamental topics in geometry (linear algebra) and algebra, acquired within the first year of the bachelor.
Readings/Bibliography
During the course notes will be handed and/or will be given exact references from textbooks.
Teaching methods
Lectures and exercises.
Assessment methods
Exam consisting of a written test and an oral test.
Students are admitted to the oral exam only if the written exam is sufficient (i.e.16/30). Both tests must be held in the same exam session.
The written exam consists of some exercises.
The final mark for the course Elementi di Algebra e Geometria da un punto di vista superiore is the average of the marks in Elementi di Algebra and in Elementi di Geometria. The mark in one of the two parts remains valid for the following 3 exam sessions (summer, winter and autumn)Office hours
See the website of Enrico Fatighenti
See the website of Fabrizio Caselli